Problem: A circle has a radius of ${3}$. An arc in this circle has a central angle of $20^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${20^\circ}$ ${3}$
First, calculate the circumference of the circle. ${20^\circ}$ ${3}$ ${6\pi}$ ${c} = 2\pi r = 2\pi ({3}) = {6\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{20}^\circ}{360^\circ} = \dfrac{{s}}{{{6\pi}}}$ $\dfrac{1}{18} = \dfrac{{s}}{{6\pi}}$ $\dfrac{1}{18} \times {6\pi} = {s}$ $\dfrac{1}{3}\pi = {s}$ ${20^\circ}$ ${3}$ ${6\pi}$ ${\dfrac{1}{3}\pi}$